Thoroughly documenting the microstructure present over large object surface areas or in large transparent or semi-transparent volumes is a long, laborious task. This is presently accomplished photographically through the use of high-resolution photography or by recording a large number of photomicrographs. Both of these techniques are disadvantgeous, however, because the depth of focus in the image plane of the object is limited for each photographic record.
This problem becomes severe if very high-resolution recordings are desired, since as the resolution of an imaging optic is increased, the depth of focus thereof decreases. Furthermore, it is often desirable to manipulate optical information coming from the subject for the purpose of enhancing detail, removing unwanted subject information, or making precise topographic and optical path measurements. These operations each require the use of specialized apparatus such as the phase-contrast or Nomarski microscopes, optical processors, and interferometers. Each requires the presence of the subject and/or a recorded image of the particular detail of interest on the subject.
Full-field documentation with relatively high resolution can be accomplished through holography. By holographically recording the subject, and then reconstructing the holographic image with the conjugate to the reference beam, a three-dimensional real image of the object is created in space. This real image can then be examined microscopically as if it were the original illuminated object. An added advantage is that a holographic system can document not only reflecting surfaces but also the microstructure inside a thick, transparent object such as optical components. Since the holographic image has no substance, a microscope can focus through the image, even to the opposite side if desired, without the need for a long focus and high quality objective required when a solid object is in the way.
Examples of previous work in holographic microscopy are disclosed in Leith and Upatnieks, "Microscopy by Wavefront Reconstruction," 55 J. Opt. Soc. Amer. 569 (1965); Toth and Collins, "Reconstruction of a Three-Dimensional Microscope Sample Using Holographic Techniques," 13 Appl. Phys. Letters 7 (1968); Briones, Heflinger and Wuerker, "Holographic Microscopy," 17 Appl. Optics 1944 (1978); and Caulfield, ed., Handbook of Optical Holography, 565 (Academic Press, 1979). The records produced are large aperture wide field of view, large depth of field, three-dimensional images of both transmitting volumes and specularly or diffuse reflecting subjects. Such work, however, has not as yet obtained both the necessary resolution and field of view for viewing and/or analyzing the microstructure of large object surface areas.
When a hologram 10 is made of a subject 12 through a lens 14 or other optical components, the image information 16 from the subject may be aberrated by the lens 14 (FIG. 1a). If the hologram 10 is repositioned accurately with respect to the lens 14, and the conjugate to the reference beam 18, i.e., the same wavefront as the reference beam but travelling in the opposite direction, is used to reconstruct the holographic image, the image rays 20 will exactly retrace the path of the original subject rays back through the optical system (FIG. 1b). This is not the same as merely turning the lens 14 around, since the information about the lens aberration is stored in the hologram 10. Therefore, the aberrations of the lens 14 will be completely compensated for upon reconstruction and the holographic image 22 will be diffraction limited.
A qualification to this claim of diffraction limitation is that vignetting of the image rays by other apertures in the system will decrease the effective diffraction limit of the system. Even on axis, a focus error aberration can cause loss of spatial frequency information, as illustrated by way of example for a typical optical telescope system in FIG. 2.
A three-lens system 24 is shown, wherein lenses 1.sub.1 and 1.sub.2 are F/1.50, 50 mm diameter, 75 mm focal length lenses, and lens 1.sub.3 is an F/1.50, 150 mm diameter, 225 mm focal length lens. Assuming the sum of the spherical aberration from lenses 1.sub.2 and 1.sub.3 to be 2 mm, the focus of the rays 26 entering the system 24 is moved from a point 28 to a point 30, 77 mm away from lens 1.sub.1. This results in a smaller, F/1.54 collection angle at lens 1.sub.1.
Therefore, with a 225 mm focal length for lens 1.sub.3, which would give an F/4.5 collection angle for lens 1.sub.3 and the system 24 as a whole if lens 1.sub.1 collected F/1.50, the lens can only collect: ##EQU1##
Similarly, for 1 mm of special aberration, the focal point is moved to 76 mm away from lens 1.sub.1 and: ##EQU2## for the system 24.
To consider these effects directly, the optical transfer function (OTF) of the system may be looked to.
For a diffraction limited system: ##EQU3## where a(f.sub.x,f.sub.y) is the area of overlap of the pupil collecting spatial frequencies with the restricting pupil function.
The OTF with aberrations for two pupils given by: ##EQU4## where W is the aberration function.
The Schwarz inequality, EQU .vertline..intg..intg.XYd.xi.d.eta..vertline..sup.2 .ltoreq.(.intg..intg..vertline.X.vertline..sup.2 d.xi.d.eta.)(.intg..intg..vertline.Y.vertline..sup.2 d.xi.d.eta.)
can be used to show directly that EQU .vertline.H(f.sub.x,f.sub.y).sub.aber. .vertline..sup.2 .ltoreq..vertline.H(f.sub.x,f.sub.y).vertline..sup.2 no aberrations
This means that aberrations never increase the MTF (the modulus of the OTF), but rather lower the contrast of each spatial frequency component. Thus, the cutoff to the spatial frequency passed by the system will be effectively decreased and the effective F-number thereof will increase. This is especially important if there is a random background to further decrease the contrast.
Off-axis, spatial frequency information can be lost even in an ideal aberration-free system directly due to vignetting, as shown in FIGS. 3 and 4. Again, considering the sample three-lens optical system 24, the limit of the system 24 is found by tracing rays from the edge of lens 1.sub.1. The angle of incidence of these rays at a point on the subject plane 34 gives the cone angle of spatial frequency information which can be collected from that point on the subject.
In FIG. 3, using a thin lens ray trace, it can be seen that only an F/9 cone can be collected by system 24 from a point 36 located 37.5 mm off the axis 37. In FIG. 4, a point 38 located 50 mm off the axis 37 is considered. Again using a thin lens ray trace, it can be seen that only an F/13.5 cone can be collected due to vignetting.
To reconstruct a high-resolution holographic real image, the maximum available spatial frequency information must be collected. If the spatial frequency information never reaches the area of the holographic plate illuminated by the reference beam, the information is lost. For this reason, a simple single-lens, single-large-aperture imaging system would seem the most promising to obtain a high-resolution reconstructed real image.
What is needed, therefore, is such a method and apparatus for production of a holographic record that can be used for documenting detailed characteristics of an object's surface or volume and that can provide for detailed three-dimensional microscopic or macroscopic examination of that object.